Powiadomienia systemowe
- Sesja wygasła!
Identyfikatory
Warianty tytułu
Wybrane rozwiązania dokładne dla cieczy Oldroyda-B przy zadanej funkcji naprężeń stycznych zależnej od czasu
Języki publikacji
Abstrakty
The velocity field and the shear stress corresponding to motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders are established by means of the Hankel transforms. The flow of the fluid is produced due to the time dependent axial shear stress applied on the boundary of the inner cylinder. The exact solutions, presented under a series form, can easily be specialized to give similar solutions for the Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material constants on the behavior of the fluid are underlined by graphical illustrations.
Pole prędkości i pole rozkładu naprężeń stycznych wywołanych ruchem cieczy Oldroyda-B umieszczonej między dwoma koncentrycznymi cylindrami wyznaczono za pomocą transformaty Hankela. Przepływ cieczy wywołano zależnym od czasu naprężeniem stycznym od zewnętrznej ściany cylindra wewnętrznego. Uzyskane rozwiązanie dokładne, ujęte w formie rozwinięcia w szereg, może łatwo być zastosowane dla przypadków szczególnych cieczy Maxwella, cieczy drugiego stopnia i nienewtonowskich przy tych samych warunkach przepływu. Na zakończenie rozważań, przedstawiono graficznie charakterystyki ruchu cieczy i wpływ parametrów materiałowych na jej zachowanie.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
549--562
Opis fizyczny
Bibliogr. 28 poz., rys.
Twórcy
autor
autor
autor
- Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan and NED University of Engineering and Technology, Department of Mathematics, Karachi, Pakistan, jqrza26@yahoo.com
Bibliografia
- 1. Bandelli R., Rajagopal K.R., 1995, Start-up flows of second grade fluids in domains with one finite dimension, Int. J. Non-Linear Mech., 30, 817-839
- 2. Bird R.B., Armstrong R.C., Hassager O., 1987, Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, Wiley, New York
- 3. Debnath L., Bhatta D., 2007, Integral Transforms and their Applications (2nd edit.), Chapman and Hall/CRC
- 4. Dunn J.E., Fosdick R.L., 1974, Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade, Arch. Ration. Mech. Anal., 56, 191-252
- 5. Dunn J.E., Rajagopal K.R., 1995, Fluids of differential type: critical review and thermodynamic analysis, Int. J. Eng. Sci., 33, 689-728
- 6. Fetecau C., 2003, The Rayleigh-Stokes problem for an edge in an Oldroyd-B fluid, C. R. Acad. Paris Ser. I, 335, 979-984
- 7. Fetecau C., 2004, Analytical solutions for non-Newtonian fluid flows in pipelike domains, Int. J. Non-Linear Mech., 39, 225-231
- 8. Fetecau C., Awan A.U., Fetecau C., 2009a, Taylor-Couette flow of an Oldroyd-B fluid in a circular cylinder subject to a time-dependent rotation, Bull. Math. Soc. Sci. Math. Roumanie, 52, 117-128
- 9. Fetecau C., Fetecau C., 2003, The first problem of Stokes for an Oldroyd-B fluid, Int. J. Non-Linear Mech., 38, 1539-1544
- 10. Fetecau C., Fetecau C., 2005, Decay of potential vortex in an Oldroyd-B fluid, Int. J. Eng. Sci., 43, 340-351
- 11. Fetecau C., Fetecau C., Imran M., 2009b, Axial Couette flow of an Oldroyd-B fluid due to a time-dependent shear stress, Math. Reports, 11, 145-154
- 12. Fetecau C., Fetecau C., Vieru D., 2007, On some helical flows of Oldroyd-B fluids, Acta Mech., 189, 53-63
- 13. Fetecau C., Imran M., Fetecau C., Burdujan I., 2010, Helical flow of an Oldroyd-B fluid due to a circular cylinder subject to time-dependent shear stresses, Z. Angew. Math. Phys., 61, 959-969
- 14. Georgiou G.C., 1996, On the stability of the shear flow of a viscoelasic fluid with slip along the fixed wall, Rheol. Acta, 35, 39-47
- 15. Hayat T., Khan M., Ayub M., 2004, Exact solutions of flow problems of an Oldroyd-B fluid, Appl. Math. Comput., 151, 105-119
- 16. Hayat T., Siddiqui A.M., Asghar S., 2001, Some simple flows of an Oldroyd-B fluid, Int. J. Eng. Sci., 39, 135-147
- 17. Jamil M., Khan N.A., Zafar A.A., 2011, Translational flows of an Oldroyd-B fluid with fractional derivatives, Comput. Math. Appl., 62, 1540-1553
- 18. Nazar M., Qamar Sultan, Athar M., Kamran M., Unsteady longitudinal flow of a generalized Oldroyd-B fluid in cylindrical domains, Commun. Nonlinear Sci. Numer. Simulat., 16, 2737-2744
- 19. Oldroyd J.G., 1950, On the formulation of rheological equations of state, Proc. Roy. Soc., London Ser. A, 38, 523-541
- 20. Rahaman K.D., Ramkissoon H., Unsteady axial viscoelastic pipe flows, J. Non-Newtonian Fluid Mech., 57, 27-38
- 21. Rajagopal K.R., Bhatnagar P.K., 1995, Exact solutions for some simple flows of an Oldroyd-B fluid, Acta Mech., 113, 233-239
- 22. Rajagopal K.R., Kaloni P.N., 1989, Continuum Mechanics and its Applications, Hemisphere Press, Washington, DC
- 23. Rajagopal K.R., Srinivasa A.R., 2000, A thermodynamical frame-work for rate type fluid models, J. Non-Newtonian Fluid Mech., 88, 207-227
- 24. Siddique I., Sajid Z., 2011, Exact solutions for the unsteady axial flow of non-Newtonian fluids through a circular cylinder, Commun. Nonlinear Sci. Numer. Simulat., 16, 226-238
- 25. Tong D.K., Liu Y.S., 2005, Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe, Int. J. Eng. Sci., 43, 281-289
- 26. Tong D.K., Wang R.H., 2005, Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe, Sci. Chin. Ser. G, 48, 485-495
- 27. Waters N.D., King M.J., 1970, Unsteady flow of an elastico-viscous liquid, Rheol. Acta, 93, 345-355
- 28. Wood W.P., 2001, Transient viscoelastic helical flows in pipes of circular and annular cross-section, J. Non-Newtonian Fluid Mech., 100, 115-126
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWM6-0029-0012